Tangent Vectors and Bézier Curves

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Covers the representation of plane curves and the nature of obtained curves.

Covers Descartes' Folium, a parametric curve with domain boundaries and tangent vector analysis.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.